Question

select the correct answer from each drop - down menu
the graph of g(x) is shown
the graph of h(x) = g(x + 5) has the same horizontal asymptote as function g and
drop - down menu options: the same vertical asymptote as function g, a vertical asymptote at x = - 7, a vertical asymptote at x = - 5, a vertical asymptote at x = 3

Explanation:

Step1: Identify g(x)'s asymptotes

From the graph, the vertical asymptote of $g(x)$ is $x=-2$, and the horizontal asymptote is $y=3$.

Step2: Analyze horizontal shift for h(x)

For $h(x)=g(x+5)$, this is a left shift of 5 units. Horizontal shifts do not change horizontal asymptotes, so $h(x)$ has the same horizontal asymptote as $g(x)$.

Step3: Calculate new vertical asymptote

To find the vertical asymptote of $h(x)$, solve $x+5=-2$.
$x=-2-5=-7$

Answer:

the same horizontal asymptote as function g and a vertical asymptote at x = -7